Critical strike
Base chance to crit in Melee For melee attacks with weapons, the chance to crit is based on agility, and critical strikes deal +100% normal damage (2.0 times your normal damage). To see your chance to crit, open your spellbook, and hover your mouse over the "attack" ability. The tooltip will show your percent chance to crit. The formula is generated as follows: * Crit + Modifier + Bonuses The base chance to achieve a melee critical hit for each class (at level 60) is: * Rogue = AGI/29% * Hunter = AGI/53% * All others = AGI/20% * Mobs always have a 5% base melee critical chance. This chance is further modified by the difference between your current Attack rating and the Defense rating of your target. The game tooltip assumes an even level opponent with a Defense rating equal to * 5. Normally, your Attack rating is equal to your skill rating with the type of weapon you are wielding. The formula is as follows: * rating - Defense Rating)/25% Please note that the agility requirement for a crit percentage is lower at lower levels... so an AGI which grants you 10% to crit at level 30 will not grant you the same at level 60. Equipment which increases critical hit rate stacks together, so it is possible to achieve relatively high critical hit rates. A non-spell attack on a sitting target will always be a critical hit. Statistically speaking, every percent of chance to crit increases your average extra damage output from crits, over time, by 1%. If you have a 1% chance to crit, you have a 1% chance to deal 100% extra damage. For average damage calcutations you can easily turn those two numbers around, so you have a 100% chance to deal 101% (100%+1%) of your base damage. It's the same considering DPS instead of damage. Note however that this is not the same as increasing your actual damage output over time by 1%, as this depends on how much crit chance you had before the +1%. Consider actual damage versus what you'd do if all swings hit and only hit for normal damage: Damage = BaseDamage * HitChanceNotIncCrit + BaseDamage * 2 * CritChance = BaseDamage * (HitChanceNotIncCrit + 2 * CritChance) Then with 100% Hit (enough +toHit to cancel default 5% miss), 5% dodge (can't be negated), 25% crit versus 26% crit: Damage = BaseDamage * ((1.00 - 0.05 - 0.25) + 2 * 0.25) = BaseDamage * 1.20 Note that with 0% crit chance this would be 0.95, so the 25% is +25% damage, when stated this way. Now, raise the crit chance by 1% Damage = BaseDamage * ((1.00 - 0.05 - 0.26) + 2 * 0.26) = BaseDamage * 1.21 That is indeed an increase of 1%. But that is only an increase of 1% to the INCREASE in damage we get from crit. This is actually only: 1.21 / 1.20 = 1.00833 i.e. 0.833% extra damage overall from +1% crit. Once you take crit-damage increasing talents, Parry, Block and Glancing Blows into account the situation is even more complex. But in general the more factors reducing the number of normal hits without decreasing the number of critical hits (i.e. if chance to hit becomes less than chance to crit your chance to crit is capped) then the more extra damage you will do for each extra 1% chance to crit. i.e. #No base miss (+5% hit or more) #5% dodge #5% parry #5% block #25% crit Damage = BaseDamage * ((1.00 - 0.05 - 0.05 - 0.05 - 0.25) + 2 * 0.25) = BaseDamage * 1.10 (With 0% crit we'd do 85% of BaseDamage) Damage = BaseDamage * ((1.00 - 0.05 - 0.05 - 0.05 - 0.26) + 2 * 0.26) = BaseDamage * 1.11 1.10 / 1.11 = 1.00909 So actually 0.0909% extra damage from +1% crit, i.e. the more you're not going to hit, the more +1% crit is worth. This does also mean that +1% crit is much more important for dual-wielding (base Hit% of 76%) than for 1h+shield, 2h or special attacks (base Hit% of 95%). Base chance to crit with Spells For spells, the chance to crit is based on intellect. Critical damage spells deal +50% (+100% with appropriate Mage/Shaman/Warlock/Druid talents) more damage. Critical heals will heal +50% their normal amount (=150%). There is currently no way to see your chance to crit with spells. The base chance for a spell critical hit for each class is : ** Druid + 1.8% ** Mage + 0.2% ** Priest + 0.8% ** Warlock + 1.7% ** Paladin ?INT/29.5?% ** Shaman + 2.3% This information was inferred from a post by Tseric, in which he revealed the expected amount of Intellect that Mages, Druids, Warlocks and Mages should have at 60, and their Intellect per Crit ratios. Knowing that at the expected amount you should have a 5% crit rate, the base crit rate can be worked out. If classes other then mages are not intended to have a 5% crit rate, this information will be incorrect. For Paladins crit chance is still unknown, thus the question marks. The estimates shown though assume 0 base crit, which in light of the new information is probably wrong. Tseric writes, "Here are some other numbers to that end: At level 60, these are expected numbers of INT and points per Crit% Warlock 200 - 60.6 Druid 192 - 60 Shaman 160 - 59.2 Priest 250 - 59.5" --------------------------------- Tests: Paladin: LumberLamer tested as a lvl 60 dwarf paladin. With 215 intellect and no crit items or talents, 566 flash of light rank 1 resulted in 35 critical heals (6.18%). Unequipped, with 76 intelligence, 20 of 576 spells were critical (3.47%). Extrapolating that would mean 0 intelligence would have 1.98% to crit, and each 51.92 INT would add 1% chance to crit. Bubblebee has also tested as a 60 dwarf paladin without crit gear and talent crit. With gear (235 intellect) on, 1000 flash of lights resulted in 77 crits. Without gear (75 intellect), 1000 flash of lights resulted in 48 crits. The results are somewhat similar to LumberLamer. 0 intellect equates to a 3.41% spell crit and approximately 54.05 intellect adds 1% spell crit. Semaj used 1200 flash of lights with no gear and 1200 with full gear. His results suggest that 0 INT would = 0% crit rate and every 29.5 INT = 1% crit for paladins. Shaman: Aryxymaraki tested the ratio using 400 casts of HW with naked int, 400 casts with half-gear, and 400 casts with full gear. He arrived at 39.5 INT = 1% crit. ---------------------------------- Quoted from this General Forum post by Tseric on May 31st, 2006 :Not exactly, but the numbers tend to hover around that mark for many casters, at least. Obviously, for melee the numbers are somewhat irrelevant. Sorry that I don't have the exact numbers for Paladins, but the trend is illustrated. Here are some other numbers to that end: :At level 60, these are expected numbers of INT and points per Crit% :Warlock 200 - 60.6 :Druid 192 - 60 :Shaman 160 - 59.2 :Priest 250 - 59.5 These is still a disconnect between the previously discussed 5% crit base and these numbers, but Blue information is always worth capturing. Can Crits miss or not? The only real source for answer of this question is this Blizzard post. There exist two ways to interprete it. One school ("Crits can miss") claims that the half-sentence "if you have a 5% crit rate, that 5% chance includes misses" means that a crit can be a miss, so if you have a 10% crit chance, and 5% miss chance, only 8 swings out of 100 will crit in the average. This means that each swing can be either a hit or a miss, and crits are calculated completely independently. The other school ("Three outcomes") claims that the mathematical formulas given later in the post make clear that crits may never miss, and that a swing can have exactly one of three outcomes - crit, hit or miss. The probability for each of these three is calculated separate, the only restriction is that their sum has to be 100%. Argument for Crits may miss There are many crit modifying spells within the game which can miss (such as Cold Blood). A way to confirm or deny this, would be to let a rogue with 300 dagger skill, no +% talents or effects, use only auto-attack on a (preferrably healing-class) player with no +def for about an hour or longer. Record his crit per swing, and compare that to the crit chance displayed in his tooltip. It is however crucial that the mod/program/whatever which is recording, only recordes crit per swing and not crit per hit. So it would have to count swings, and count crits, and then divide the first by the later. Then redo the entire thing with, respectively, more %hit and more %crit. Argument for three outcomes The counter-argument to the "cold blood may miss" argument is that you may never increase your crit chance at the cost of your miss chance, i.e. if you have a 5% miss chance, you crit chance cannot increase beyond 95%. Using cold blood only guarntees that you will never see a normal hit, it does nothing to your miss chance. Interpreting the blizzard post with the following steps: # "The crit rate includes misses" is a contradiction to the assumption that crits, hits and misses are the three possible, separate outcomes of a swing. # Replacing "misses" by "swings that do not hit" yields: "The crit rate includes swings that do not hit". # This version of the sentence matches the formulas This rather formal way of interpretation assumes a little slip in the natural language used by Blizzard. If there are three different outcomes, replacing "miss" with "not a hit" is mathematically a severe error. In natual language though it's only a slight imprecision. In other words, Blizzard uses the term "miss" a little loose, they mean it to include all swings which are not normal hits. Chances to Crit, Hit and Miss Thus we assume that melee attack can have exactly one of the following results: *Critical Hit *Normal Hit *Miss The probabilities for these three results are independent of each other, except for the requirement that the sum must be 100%. If the game's tooltip says a character's critical hit rate is 5%, they will crit 5% of all attacks (vs. an opponent with the same defense skill as the attacker's weapon skill). Modifier to Crit Plusses to Crit simply affect the probability to acheive a critical hit. They do nothing to the miss rate, thus they decrease the Hit rate. This seems to be strange at first, but it's WoW's way to express the concept that critical hits must also be normal hits. The difference between opponents defense skill and attackers weapon skill will modify the critical hit chance by 0.04% per point of difference. So, for example, if a Rogue with 300 dagger skill is attacking a Mob with 325 defense skill, the rogue's crit rate will be decreased by 1%. Be aware though that +Defense in this context does not apply to PvP. It will not reduce a critical hit chance between players, only vs. PvE mobs. Modifier to Hit Plusses to Hit in increase the probability to get a non-critical hit. They do nothing to your chance to Crit and they decrease your chance to Miss. In fact, one might argue that "+hit%" is a misnomer, and that such bonuses really ought to be called "-miss%". The base miss chance vs. an even level opponent is 5%. It is modified by the level difference. It rises quickly for mobs in PvE, but it rises much more slowly for other characters in PvP. The minimum miss chance is 0% on instant attacks. For each increased weapon skill you get 0.04% less miss chance, but for each defence point the target has, your miss chance is increased by 0.04%. So against a level 63 mob, you would maximum want +5.6% hit, and for dual wielders you would maximum want +24.6% hit. The cap for the miss chance is 60% (this cap is not confirmed. Can anyone add a link or elaborate?). If due to large negative modifiers, your chance to Hit becomes negative, the negative amount is deducted from your chance to Crit. (If your chance to Crit would also become negative, the remaining negative amount is deducted from your chance to score a Glancing Blow, if any. See the Attack table article.) Defensive Reactions WoW, like many other games, makes use of a table based combat scheme (where one roll determines the outcome of a swing), so percentages are absolute. Refer to the separate section for details on each defensive reaction: # Parry # Dodge # Block You will not get terribly wrong results by simply adding the targets chances to parry and dodge to the attackers miss chance. Formulas for Melee combat If adding some crit or hit modifier, the following formulas can be used: *New crit rate = (Original crit%) + (change to crit %) *New miss rate = (Original miss%) - (change to hit%) *New hit rate = (Original hit%) - (change to crit %) + (change to hit) What's better: +Hit% or +Crit% with spells? Spell crits do +50% spell damage unless you talent to increase this effect. Spell hits do +100% spell damage. So in terms of total damage output the +hit with spells will be more efficient until you have reduced your chance to miss that mob to the minimum. If you have talents such as Ruin or ice shards that increase crit damage then the total added damage is almost the same and +crit and +hit are equivalent in terms of damage added. That being said, keep in mind the situation. If you want burst damage such as PvP encounters it may be better to have +crit, and in PvE encounters where aggro must be avoided it would be better to have +hit. Unlike melee, there is a 99% hit cap on spells. Spell casts against a same level mob or player have a 96% hit (no resist) chance, so +hit equipped past 3% in this case is wasted. Level 63 mobs have an 83% hit chance, so +hit equipped past 16% would be wasted. The only limit to crit is 100%, but bear in mind that the spell cast system does not combine hit and crit calculations into a single roll. A spell must hit in order for it to have a chance to crit. However, some spells and schools have talents which proc additional effects on crit. For example, mages can put talent points in ignite, which grants an addition 40% damage over time on crit. Warlocks can put talent points in Improved Shadowbolt, which grants an additional 20% damage to the next 4 sources of shadow damage. The effect of these procs are to increase the damage bonus of a crit beyond 100% over time, which means that in some cases additional +crit yields a greater average increase in damage than +hit. The decision between equipping +crit and +hit is further complicated when procs can be resisted, and also depend on the currently equipped +crit and +hit. It is known that Improved Shadowbolt can be resisted, and it is thought that this is based on standard Binary Spell resistance, which is mitigated by +hit. The same is probably true for other procs. In the case of vulnerability procs which require refreshing and have limited duration/charges, +hit comes back into favour as it allows the proc to stay active on the target for a greater proportion of time. It is also worth noting that in a raid, keeping these procs active will also increase the damage of all other casters using that spell school. In general, if you do not have a talent to increase spell crit bonus to 100%, then +hit is far better than +crit (until you run into the hit cap). If you have talents to increase spell crit bonus and/or proc additional effects, then +hit is of roughly equal value to +crit. It should be noted, however, that benificial spells cast on friendly targets (such as heals and buffs) always hit, regardless of +hit gear. If your role in groups is primarily healing (i.e. if you are a holy priest or paladin, or a restoration druid or shaman) then you will gain much more benefit from gear that increases your spell crit chance. Although it is not advisable to rely on the extra healing granted by critical effects from healing spells, a lucky critical heal may mean the difference between life and death for a group member. Additionally, there are talents available to Priests and Shamans which grant a temporary armor bonus to the recipient of a critical heal, which in essence increases the effect of a healing spell even further by reducing the physical damage taken by that party member. When given the choice between +hit and +crit, a primary healer will always benefit from more +crit. What's better: +Hit% or +Crit% with physical? If you're only going to be attacking mobs of the same level from behind, and you don't dual wield, your attack tables will look like this: Now assume your weapon does 100 points of base damage, before modification, you will do (5 * 200 + 80 * 100) = 9000 damage over 100 swings. With +5% to crit, the result is (10 * 200 + 75* 100) = 9500 damage over 100 swings. With 5% to hit, the damage figure is (5 * 200 + 85 * 100) = 9500 damage over 100 swings. So all other things being equal, in this case, increasing your probabilities to hit or to crit increase your average damage output by exactly the same amount. Useful differences would only arise from effects which require hits or crits (like some abilities or procs). However, real combat is rarely done against equal-level mobs from behind without dual wielding. Consider the following table, which represents a melee attack made against a boss mob (effectively level 63) by a level 60 dual-wielder from the front: While it's true here that +5% crit adds as much average melee damage as +5% hit, adding more +crit% gear will soon result in a kind of "crit cap". With no +hit% bonus, adding +crit% bonuses beyond a total of 14.2% will not increase the attacker's actual chance to crit against that target. If this attacker had more than +14.2% of total +crit bonuses, adding +hit% gear would actually increase his crit chance! This makes more sense when you realize that so-called "+hit" gear doesn't so much increase your hit chance as decrease your miss chance. If you are not dual-wielding, or if you are using an instant attack or "special" attack such as Sinister Strike or Heroic Strike, your base chance to miss an equal-level target is only 5%, and your chance to miss a boss mob (if you're level 60) will be, at most, 5.6%. The common consensus is that +6% is the desirable maximum for +hit% unless you are a dual-wielder. See Formulas:Weapon_Skill and Attack table. Examples Let's say a rogue with 300 weapon skill attacks an opponent with 310 defense skill. The rogue has a base 20% crit chance, a 25% miss chance and then the rogue equips items that give an additional +5% toHit and +5% crit. The victim has a 10% chance to dodge, a 10% chance to parry, but doesn't have a sheild. This will result in the following: *Crit: 20% + (-0.4%) + 5% = 24.6% *Miss: 25% - 5% + 10% + 10% = 40% *Hit: 55% - (-0.4%) + 5% - 5% - 10% - 10% = 35.4% If the victim was rogue who activated Evasion, his dodge chance would jump by 50%. If the attacker was also a rogue, and activated Improved Backstab his crit rate would jump by 30% crit rate, the numbers would become: *Crit: 24.6% + 30% = 54.6% *Miss: 40% + 50% = 90% *Hit: 35.4% - 30% - 50% = -44.6% Obviously the new numbers make no sense. That's because the miss chance is capped at 60% and when there is no chance of score a regular hit, miss chance will consume crit chances. So in the case the numbers get modified by the caps: *New crit chance: 40% *New miss chance: 60% *New hit chance: 0% This example doesn't actually work, because backstab must be performed from behind the target and characters can't dodge, parry or block attacks from behind (but note a mob/creature can dodge with you behind it, c.f. 1.3 Patch Notes). Further Input Kitsunei, lvl 60 Rogue found the following: In endgame PvE (Molten Core and beyond), +hit and +crit are not equal. +Weapon Skill also becomes more useful at this stage. The reason for this are the "glancing blows". Lvl 63+ mobs and bosses have a 70-75% chance that your white damage gets reduced (which is most upsetting for rogue builds concentrating on white damage). There are two aspects with glancing blows: Their frequency, and their amount of damage reduction. +10 weapon skill should suffice to cancel all damage reduction from glancing blows. Weapon skill may also help to reduce the frequency, but not by a large amount. The problem is that glancing blows are a fourth possible outcome, and that they take precedence over the crit rate. Assume a Rogue has a 70% glancing blows, 10% miss and 30% Crit. This rogue will never produce a normal hit. The actual numbers resulting will be 10% miss, 70% glancing, and only 20% Crit, 10% critrate are wasted. It would be much smarter to use more +hit gear, and/or to reduce the probability for glancing. Links This Blizzard post is the base of all our knowledge. Slant's To-Hit FAQ can be found in the Ultimate Rogue FAQ. Mizzajl's Critical_hit_table. Category:Formulas and Game Mechanics